Existence and non-uniqueness of similarity solutions of a boundary layer problem

A Blasius boundary value problem with inhomogeneous lower boundary conditions f(0) = 0 and f'(0) = - lambda with lambda strictly positive was considered. The Crocco variable formulation of this problem has a key term which changes sign in the interval of interest. It is shown that solutions of the boundary value problem do not exist for values of lambda larger than a positive critical value lambda. The existence of solutions is proven for 0 lambda lambda by considering an equivalent initial value problem. It is found however that for 0 lambda lambda, solutions of the boundary value problem are nonunique. Physically, this nonuniqueness is related to multiple values of the skin friction

Acoustic Imaging by Wavefront Reconstruction

A reconstruction of the ultrasonic scattered fields in the zone near the scatter constitutes an image of the scatterer or flaw. In a real case the reconstruction zone may contain more than one distinct scatterer and accordingly the entire group form the image. At a remote location the scattered fields form a complicated diffraction pattern which will yield the image if operated on by a suitable set of mathematical operations. The measurement of the remote fields is of major interest as it affects the image quality. Unlike phased array systems, the transducer spacing, hence measurement sampling density, is determined by the spatial frequencies of the diffraction pattern and sampling theory. This paper will describe the implementation of a 64 x 64 2D array and the results obtained in imaging the phase and magnitude of source and scattered fields

Modern considerations for the use of naive Bayes in the supervised classification of genetic sequence data

2021 Spring.Includes bibliographical references.Genetic sequence classification is the task of assigning a known genetic label to an unknown genetic sequence. Often, this is the first step in genetic sequence analysis and is critical to understanding data produced by molecular techniques like high throughput sequencing. Here, we explore an algorithm called naive Bayes that was historically successful in classifying 16S ribosomal gene sequences for microbiome analysis. We extend the naive Bayes classifier to perform the task of general sequence classification by leveraging advancements in computational parallelism and the statistical distributions that underlie naive Bayes. In Chapter 2, we show that our implementation of naive Bayes, called WarpNL, performs within a margin of error of modern classifiers like Kraken2 and local alignment. We discuss five crucial aspects of genetic sequence classification and show how these areas affect classifier performance: the query data, the reference sequence database, the feature encoding method, the classification algorithm, and access to computational resources. In Chapter 3, we cover the critical computational advancements introduced in WarpNL that make it efficient in a modern computing framework. This includes efficient feature encoding, introduction of a log-odds ratio for comparison of naive Bayes posterior estimates, description of schema for parallel and distributed naive Bayes architectures, and use of machine learning classifiers to perform outgroup sequence classification. Finally in Chapter 4, we explore a variant of the Dirichlet multinomial distribution that underlies the naive Bayes likelihood, called the beta-Liouville multinomial. We show that the beta-Liouville multinomial can be used to enhance classifier performance, and we provide mathematical proofs regarding its convergence during maximum likelihood estimation. Overall, this work explores the naive Bayes algorithm in a modern context and shows that it is competitive for genetic sequence classification

Characterization of NDE Transducers

Characterization of NDE transducers is an important part of current and future programs in quantative flaw detection. In the work reported here, emphasis has been placed on beam pattern measurements or profiling and circuit modeling of the transducer using electrical network scattering parameters, or S-parameters. The latter topic is relatively new and was developed in the last six to eight months in order to handle the problems of existing commercial transducers whose internal details are unknown. A subset of this goal is to: {a) explore single crystal or very high quality ceramic materials as the piezoelectric element, (b) examine the single disk in water as a transducer or reference element, and (c) look into electrical loading as an alternative to mechanical loading

On similarity solutions of a boundary layer problem with an upstream moving wall

The problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream is examined. It was previously shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream. In particular, it was proved that a solution exists only if this parameter does not exceed a certain critical value, and numerical evidence was adduced to show that this solution is nonunique. Using Crocco formulation the present work proves this nonuniqueness. Also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter

Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations

In this article, we study the self-similar solutions of the 2-component Camassa-Holm equations% \begin{equation} \left\{ \begin{array} [c]{c}% \rho_{t}+u\rho_{x}+\rho u_{x}=0 m_{t}+2u_{x}m+um_{x}+\sigma\rho\rho_{x}=0 \end{array} \right. \end{equation} with \begin{equation} m=u-\alpha^{2}u_{xx}. \end{equation} By the separation method, we can obtain a class of blowup or global solutions for $\sigma=1$ or $-1$. In particular, for the integrable system with $\sigma=1$, we have the global solutions:% \begin{equation} \left\{ \begin{array} [c]{c}% \rho(t,x)=\left\{ \begin{array} [c]{c}% \frac{f\left( \eta\right) }{a(3t)^{1/3}},\text{ for }\eta^{2}<\frac {\alpha^{2}}{\xi} 0,\text{ for }\eta^{2}\geq\frac{\alpha^{2}}{\xi}% \end{array} \right. ,u(t,x)=\frac{\overset{\cdot}{a}(3t)}{a(3t)}x \overset{\cdot\cdot}{a}(s)-\frac{\xi}{3a(s)^{1/3}}=0,\text{ }a(0)=a_{0}% >0,\text{ }\overset{\cdot}{a}(0)=a_{1} f(\eta)=\xi\sqrt{-\frac{1}{\xi}\eta^{2}+\left( \frac{\alpha}{\xi}\right) ^{2}}% \end{array} \right. \end{equation} where $\eta=\frac{x}{a(s)^{1/3}}$ with $s=3t;$ $\xi>0$ and $\alpha\geq0$ are arbitrary constants.\newline Our analytical solutions could provide concrete examples for testing the validation and stabilities of numerical methods for the systems.Comment: 5 more figures can be found in the corresponding journal paper (J. Math. Phys. 51, 093524 (2010) ). Key Words: 2-Component Camassa-Holm Equations, Shallow Water System, Analytical Solutions, Blowup, Global, Self-Similar, Separation Method, Construction of Solutions, Moving Boundar

Promoting post-stroke recovery through focal or whole body vibration: criticisms and prospects from a narrative review

Objective: Several focal muscle vibration (fMV) and whole body vibration (WBV) protocols have been designed to promote brain reorganization processes in patients with stroke. However, whether fMV and WBV should be considered helpful tools to promote post-stroke recovery remains still largely unclear. Methods: We here achieve a comprehensive review of the application of fMV and WBV to promote brain reorganization processes in patients with stroke. By first discussing the putative physiological basis of fMV and WBV and then examining previous observations achieved in recent randomized controlled trials (RCT) in patients with stroke, we critically discuss possible strength and limitations of the currently available data. Results: We provide the first systematic assessment of fMV studies demonstrating some improvement in upper and lower limb functions, in patients with chronic stroke. We also confirm and expand previous considerations about the rather limited rationale for the application of current WBV protocols in patients with chronic stroke. Conclusion: Based on available information, we propose new recommendations for optimal stimulation parameters and strategies for recruitment of specific stroke populations that would more likely benefit from future fMV or WBV application, in terms of speed and amount of post-stroke functional recovery

C.H.E. Det Optimisme, disiplin dan wawasan

Optimisme, disiplin dan wawasan. Tiga perkataan ini cukup untuk menggambarkan kualiti beliau. Optimisme – kepercayaan teguh beliau bahawa cita-cita yang diisi akan menatijahkan kejayaan, dan tanpa pengisian, cita-cita tersebut sekadar tinggal angan-angan. Disiplin – tunjang prinsip beliau bahawa usaha ke arah kecemerlangan menuntut sikap dan watak yang khusus, dan tanpa disiplin, kegagalan pasti menanti. Wawasan – pandangan jauh beliau bahawa kejayaan sebenar terletak kepada keupayaan untuk melestarikan pencapaian di atas garis masa yang panjang. 87 tahun usia yang bakal dilewati tanggal 20 Disember kelak, dan tiga kualiti ini – DISIPLIN, OPTIMISME dan WAWASAN terus segar mendasari penyandang keempat jawatan Perdana Menteri Malaysia, Tun Dr. Mahathir Mohamad